……Adam Chlipala 写的（“FRAP”）——可以在这里免费获取：http://adam.chlipala.net/frap/。它是 MIT 6.822 课程的基础教材，还配套了 Coq 形式化代码（以及 Coq 写的作业题 psets）。* Glynn Winskel 的《The Formal Semantics of Programming Languages: An Introduction》。
…("FRAP") by Adam Chlipala - available for free here: http://adam.chlipala.net/frap/. Forms the basis for 6.822 at MIT, and comes with an accompanying Coq formalisation (as well as psets in Coq). * The Formal Semantics of Programming Languages: An Introduction by Glynn Winskel.
Glynn Winskel 的《The Formal Semantics of Programming Languages》（1993年）——虽然有点年头了，但依然写得非常好。涵盖了基础语义学/类型论。Benjamin Pierce 的《Types and Programming Languages》（2002年）——你懂的，就是你手边最基础的类型论宝典。Benjamin Pierce 的《Advanced…
Glynn Winskel, "The Formal Semantics of Programming Languages", 1993 -- a bit dated but still quite good. Covers basic semantics/type theory. Benjamin Pierce, "Types and Programming Languages", 2002 -- y'know, just your basic type theory. Benjamin Pierce, "Advanced…
……然后证明这个定义等价于操作语义的定义。在一些优秀的教材里（比如 Winskel 的《The Formal Semantics of Programming Languages》），已经针对玩具语言给出了这种证明的非形式化版本。现在差的只是把它扩展到 C 语言级别，并向下落实到形式化验证的层面。我还想指出的是，目前有一个正在进行的研究项目也采用了同样的路径，即“基于抽象解释的……
…then prove that this definition is equivalent to the operational semantics definition. An informal version of this proof for a toy language already exists in good textbooks (for instance Winskel's The Formal Semantics of Programming Languages). It is just a matter of scaling up to C and scaling down to the formally verified level. I should also point out that there is an ongoing research project that takes the same approach, with “Abstract-interpretation-based…
不，我倒不觉得范畴论是学域论（domain theory）的普适前置条件。我对域论最熟悉的部分来自 Winskel 的《Formal Semantics of Programming Languages》（一本神书，在附带的 PDF 中被引用为 Win93），里面整整有一章讲这个主题，却完全没提范畴论。但如果你要更深入地研究域论（比如啃完这本书）……
No, I wouldn't say that category theory is a prerequisite for domain theory in general. I'm most familiar with domain theory from Winskel's "Formal Semantics of Programming Languages" (great book, cited as Win93 in the linked PDF), which has a whole chapter on the subject with no reference to category theory. If you get deeper into domain theory (e.g. by working through this book)…
……补充材料：- Michael Huth 和 Mark Ryan，《Logic in Computer Science: Modelling and Reasoning about systems》（第2版），剑桥大学出版社 2004 年。（主要是第 1、2 章）- Glynn Winskel，《The Formal Semantics of Programming Languages: An Introduction》，MIT 出版社 1993 年。（主要是第 1、2、3、6、11 章）- Benjamin C. Pierce，《Types and Programming Languages》，MIT 出版社 2002 年。（主要是第 5、8、9、11、12 章）
…supplementary material: - Michael Huth and Mark Ryan. Logic in Computer Science: Modelling and Reasoning about systems (2nd ed.). Cambridge University Press 2004. (Mainly chapters 1, 2) - Glynn Winskel. The Formal Semantics of Programming Languages: An Introduction, MIT Press 1993. (Mainly chapters 1, 2, 3, 6, 11) - Benjamin C. Pierce. Types and Programming Languages. MIT Press 2002. (Mainly chapters 5, 8, 9, 11, 12)
It's nice to see theorem proving gain some momentum in a mainstream mathematics topic such as analysis. In PLT, we already had a flagship book (The Formal Semantics of Programming Languages by Winskel) formally verified (kind of, it's not a 1-to-1 transcription) using Isabelle (http://concrete-semantics.org) back in the mid 2010s, when tools began to be very polished. IMHO, if someone is…
……Adam Chlipala 写的（“FRAP”）——可以在这里免费获取：http://adam.chlipala.net/frap/。它是 MIT 6.822 课程的基础教材，还配套了 Coq 形式化代码（以及 Coq 写的作业题 psets）。* Glynn Winskel 的《The Formal Semantics of Programming Languages: An Introduction》。
…("FRAP") by Adam Chlipala - available for free here: http://adam.chlipala.net/frap/. Forms the basis for 6.822 at MIT, and comes with an accompanying Coq formalisation (as well as psets in Coq). * The Formal Semantics of Programming Languages: An Introduction by Glynn Winskel.
Glynn Winskel 的《The Formal Semantics of Programming Languages》（1993年）——虽然有点年头了，但依然写得非常好。涵盖了基础语义学/类型论。Benjamin Pierce 的《Types and Programming Languages》（2002年）——你懂的，就是你手边最基础的类型论宝典。Benjamin Pierce 的《Advanced…
Glynn Winskel, "The Formal Semantics of Programming Languages", 1993 -- a bit dated but still quite good. Covers basic semantics/type theory. Benjamin Pierce, "Types and Programming Languages", 2002 -- y'know, just your basic type theory. Benjamin Pierce, "Advanced…
……然后证明这个定义等价于操作语义的定义。在一些优秀的教材里（比如 Winskel 的《The Formal Semantics of Programming Languages》），已经针对玩具语言给出了这种证明的非形式化版本。现在差的只是把它扩展到 C 语言级别，并向下落实到形式化验证的层面。我还想指出的是，目前有一个正在进行的研究项目也采用了同样的路径，即“基于抽象解释的……
…then prove that this definition is equivalent to the operational semantics definition. An informal version of this proof for a toy language already exists in good textbooks (for instance Winskel's The Formal Semantics of Programming Languages). It is just a matter of scaling up to C and scaling down to the formally verified level. I should also point out that there is an ongoing research project that takes the same approach, with “Abstract-interpretation-based…
不，我倒不觉得范畴论是学域论（domain theory）的普适前置条件。我对域论最熟悉的部分来自 Winskel 的《Formal Semantics of Programming Languages》（一本神书，在附带的 PDF 中被引用为 Win93），里面整整有一章讲这个主题，却完全没提范畴论。但如果你要更深入地研究域论（比如啃完这本书）……
No, I wouldn't say that category theory is a prerequisite for domain theory in general. I'm most familiar with domain theory from Winskel's "Formal Semantics of Programming Languages" (great book, cited as Win93 in the linked PDF), which has a whole chapter on the subject with no reference to category theory. If you get deeper into domain theory (e.g. by working through this book)…
……补充材料：- Michael Huth 和 Mark Ryan，《Logic in Computer Science: Modelling and Reasoning about systems》（第2版），剑桥大学出版社 2004 年。（主要是第 1、2 章）- Glynn Winskel，《The Formal Semantics of Programming Languages: An Introduction》，MIT 出版社 1993 年。（主要是第 1、2、3、6、11 章）- Benjamin C. Pierce，《Types and Programming Languages》，MIT 出版社 2002 年。（主要是第 5、8、9、11、12 章）
…supplementary material: - Michael Huth and Mark Ryan. Logic in Computer Science: Modelling and Reasoning about systems (2nd ed.). Cambridge University Press 2004. (Mainly chapters 1, 2) - Glynn Winskel. The Formal Semantics of Programming Languages: An Introduction, MIT Press 1993. (Mainly chapters 1, 2, 3, 6, 11) - Benjamin C. Pierce. Types and Programming Languages. MIT Press 2002. (Mainly chapters 5, 8, 9, 11, 12)
很高兴看到定理证明在像分析学这样的主流数学领域里也开始受到关注了。在编程语言理论（PLT）圈子里，早在 2010 年代中期工具链开始变得非常成熟的时候，我们就已经有一本标杆级著作（Winskel 的《The Formal Semantics of Programming Languages》）用 Isabelle 进行了形式化验证（差不多算吧，并不是百分之百一对一的形式化翻译），参考 http://concrete-semantics.org。依我看，如果有人……
It's nice to see theorem proving gain some momentum in a mainstream mathematics topic such as analysis. In PLT, we already had a flagship book (The Formal Semantics of Programming Languages by Winskel) formally verified (kind of, it's not a 1-to-1 transcription) using Isabelle (http://concrete-semantics.org) back in the mid 2010s, when tools began to be very polished. IMHO, if someone is…